A train starts from rest at `S = 0` and is subjected to an acceleration as shown in figure. Then,

Options

A. velocity at the end of 10 m displacement is `20 ms^-1`
B. velocity of the train at `S = 10 m` is `10 ms^-1`
C. The maximum velocity attained by train is `sqrt180 ms^-1`
D. The maximum velocity attained by the train is 15 ms^-1

Answer

B, C

Explanation

a-s equation corresponding to given graph is,
`a=6-s/5`
`:. v.(dv)/(ds)=(6-s/5)`
or `int_0^v v dv=int_0^s(6-s/5)ds`
or `v=sqrt(125-(s^2)/5)`
At `s=10m, v=10m//s`
Maximum values of v is obtained when
`(dv)/(ds)=0 which gas s=30m`
`:. v_(max)=sqrt(12xx30-(30)^2/5)`
`=sqrt180 m//s`